Construction of Perfect Auto-correlation Arrays and Zero Cross-correlation Arrays from Discrete Projections

Abstract

This paper presents a new method by which sets of discrete 1D projections can be used to construct large families of 2D discrete arrays. These compact arrays have targeted, specific periodic correlation values that span the full range between perfect auto-correlation to zero cross-correlation. The array size is variable and the array elements can be binary or contain grey integer values. Arrays with these properties are useful for digital signal synchronisation, communications and watermarking. We show that multiple copies of zero cross-correlation arrays can be co-located without interference and that the presence of individual arrays is able to be determined independently. The arrays with perfect periodic auto-correlation also have high aperiodic auto-correlation and optimally low cross-correlation, making them well-suited for use as digital watermarks.